E-Commerce Security Systems - Formula Sheet

E-Commerce Security Systems - Formula Sheet

1. Key Management Scaling (Symmetric Cryptography)

Formula: K_sym = N * (N - 1) / 2

Definitions:

• K_sym: Total number of symmetric keys required for secure communications in a closed network.
• N: Total number of active users in the system.

Significance: This shows that symmetric key management scales quadratically, making it difficult to distribute keys safely for very large groups of users.

2. Key Management Scaling (Asymmetric Cryptography)

Formula: K_asym = 2N

Definitions:

• K_asym: Total number of keys required.
• N: Total number of active users.

Significance: Because each user only requires a public key and a private key, the key count scales linearly, making management much simpler.

3. Secure Sockets Layer (SSL) Session Key Exchange

Formula: S(P(K)) = K

Definitions:

• K: Symmetric session key generated randomly by the user's browser.
• P: Server's public key extracted from its digital certificate.
• S: Server's private key held securely on the host server.
• P(K): Session key encrypted with the server's public key.

Significance: This demonstrates how asymmetric cryptography is used to securely pass a temporary symmetric key. Only the server holding private key S can reverse P(K) to retrieve K.

4. Check Digit Validation (Luhn Algorithm)

Formula: Sum(d_i) mod 10 = 0

Definitions:

• d_i: The adjusted digits of the card number from right to left.
• Sum(d_i): The sum of all digits after doubling every second digit starting from the right. If doubling a digit results in a number greater than 9, subtract 9 from it first.

Significance: This is the mathematical check used to detect simple typing errors in payment card numbers.